Quality Control Chapter 10 - McGraw Hill Education ✓ Solved

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Identify potential process problems related to the supplier’s production of nozzle diameters and discuss analysis methods and conclusions regarding process issues using sample data and control charts. Explain whether a run test was performed and justify your reasoning.

Sample Paper For Above instruction

The primary aim of this analysis is to evaluate whether the supplier’s manufacturing process for nozzle throat diameters exhibits any process problems that could affect the performance of Poindexter’s Rat-Freeze traps. Based on the context provided, potential process issues could include a lack of consistency in product quality, variability exceeding specification limits, or a shift or trend indicating instability of the process. These issues can adversely impact the product’s ability to reliably freeze rats moving more than an inch, thereby threatening customer satisfaction and corporate reputation.

One possible problem is that the process may be out of control due to variability that exceeds the acceptable limits. To analyze this, the first dataset consisting of 50 individual nozzle diameters, which are normally distributed, can be examined via a control chart for individual measurements. Calculating the mean and standard deviation from this data allows us to construct control limits. If the process is indeed stable, all individual observations should fall within the control limits, and no non-random patterns should be evident. Such analysis confirms whether the process is capable of producing within-specification diameters consistently, indicating stable operation.

A second potential issue concerns whether the process is centered within the specifications, which are set at 0.1000 ± 0.0050. To investigate this, the sample mean from the 50 measurements should be compared to the target value, and process capability indices such as Cp and Cpk should be calculated. If the mean is significantly shifted away from the target or the capability indices are below acceptable thresholds, it suggests the process may be skewed or poorly controlled, risking the production of out-of-specification nozzles.

Using the second dataset comprising 20 samples of size 5, a typical approach involves constructing X̄ and R control charts to monitor process stability over time. The sample means provide insight into the central tendency, while the ranges indicate process dispersion. Establishing control limits based on initial data (if the process was under control) aids in detecting shifts or trends in the process. If values fall outside these limits, it suggests non-random variation, hinting at potential process problems that need correction before further production.

Regarding the second question, a run test is often performed when control chart analysis indicates an in-control process, but there is suspicion of non-random patterns such as trends or cycles. In this case, if residual patterns or sequences in the data suggest possible systematic issues, a run test can help confirm whether the observed patterns are statistically significant or simply due to randomness. If no such suspicion exists or control charts show no out-of-control signals, a run test may not be necessary.

In conclusion, potential process problems include variability outside acceptable limits, process shifts, and non-centered production relative to specifications. Control chart analyses of both datasets serve as effective tools to detect these issues. If data indicate stability and capability, then the process is likely under control; otherwise, corrective actions are warranted. Whether a run test was performed depends on the control chart results and the analyst’s judgment regarding patterns, with such tests offering an additional layer of confirmation for process stability.

References

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• Antony, J., & Bhattacharya, S. (2019). Lean Six Sigma for Manufacturing. Productivity Press.
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